Question: Express your answer as a mixed number simplified to lowest terms. $19\dfrac{2}{6}-12\dfrac{5}{12} = {?}$
Solution: Simplify each fraction. $= {19\dfrac{1}{3}} - {12\dfrac{5}{12}}$ Find a common denominator for the fractions: $= {19\dfrac{4}{12}}-{12\dfrac{5}{12}}$ Convert ${19\dfrac{4}{12}}$ to ${18 + \dfrac{12}{12} + \dfrac{4}{12}}$ So the problem becomes: ${18\dfrac{16}{12}}-{12\dfrac{5}{12}}$ Separate the whole numbers from the fractional parts: $= {18} + {\dfrac{16}{12}} - {12} - {\dfrac{5}{12}}$ Bring the whole numbers together and the fractions together: $= {18} - {12} + {\dfrac{16}{12}} - {\dfrac{5}{12}}$ Subtract the whole numbers: $=6 + {\dfrac{16}{12}} - {\dfrac{5}{12}}$ Subtract the fractions: $= 6+\dfrac{11}{12}$ Combine the whole and fractional parts into a mixed number: $= 6\dfrac{11}{12}$